Daytrading and being a trader......instead of being BOB

Greetings
Recently, in our chat room somebody asked why we use Standard Error Price Bands as opposed to Standard Deviation Bands, ala Bollinger Bands and what is the difference. I always try to avoid those discussions because it gets very complicated ... very complicated. In fact, it confuses the issue more than anything else, but, for those of you having trouble sleeping at night we'll explore the differences between standard deviation and the standard error of a value.

In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is a measure of the spread of its values. It is defined as the square root of the variance. In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is a measure of the spread of its values. It is defined as the square root of the variance. The standard deviation is the root mean square (RMS) deviation of the values from their arithmetic mean. For example, in the population {4, 8}, the mean is 6 and the standard deviation is 2. This may be written: {4, 8} ≈ 6±2. In this case 100% of the values in the population are within one standard deviation of the mean.

Standard deviation is the most common measure of statistical dispersion, measuring how widely spread the values in a data set are. If the data points are all close to the mean, then the standard deviation is close to zero. If many data points are far from the mean, then the standard deviation is far from zero. If all the data values are equal, then the standard deviation is zero.

In statistics, a confidence interval (CI) for a population parameter is an interval between two numbers with an associated probability p which is generated from a random sample of an underlying population, such that if the sampling was repeated numerous times and the confidence interval recalculated from each sample according to the same method, a proportion p of the confidence intervals would contain the population parameter in question. Confidence intervals are the most prevalent form of interval estimation. It must be noted that a confidence interval is not in general equivalent to a (Bayesian) credible interval. The common error of equating the two is known as the prosecutor's fallacy. If U and V are statistics (i.e., observable random variables) whose probability distribution depends on some unobservable parameter θ and being divided by x (where x is a number between 0 and 1) then the random interval (U, V) is a "(100·x)% confidence interval for θ". The number x (or 100·x%) is called the confidence level or confidence coefficient. In modern applied practice, most confidence intervals are stated at the 95% level (Zar 1984).

In statistics, the standard error of a value is the estimated standard deviation of the process by which it was generated, including adjusting for sample size. In other words the standard error is the standard deviation of the sampling distribution of the sample statistic (such as sample mean, sample proportion or sample correlation). The notation for standard error can be any one of SE, SEM (for standard error of measurement or mean), or SE. Standard errors provide simple measures of uncertainty in a value and are often used because:

* If the standard error of several individual quantities is known then the standard error of some function of the quantities can be easily calculated in many cases;
* Where the probability distribution of the value is known, they can be used to calculate an exact confidence interval; and
* Where the probability distribution is unknown, relationships like Chebyshev’s or the Vysochanskiï-Petunin inequality can be used to calculate a conservative confidence interval
* As the sample size tends to infinity the central limit theorem guarantees that the sampling distribution of the mean is asymptotically normal.

Well, alrighty then! I hope that clarifies the difference between Standard Deviation and Standard Error analysis and now you can see why we are using standard error price bands and why I stay out of chat rooms these days.